Determination of Trapped Modes on a Two-Cell 1.5-GHz Superconducting Radio-Frequency Cavity

Higher order modes of a superconducting radio-frequency (SRF) cavity are typically conducted through the beam pipes to the microwave absorbers on both sides of the cavity to eliminate disturbances to the beam behavior. The cutoff frequency of the beam pipe is designed to be lower than the higher-order modes to reduce the trapped modes as much as possible. However, some modes are trapped inside the cavity even though their resonance frequencies are much higher than the cutoff frequencies of the beam pipes. In this study, we develop a numerical process to efficiently determine the trapped modes. Illustrated with a two-cell 1.5 GHz SRF cavity, the numerical results show there are eight trapped modes below 3.5 GHz. To prove the computation accuracy, the resonance frequencies of a two-cell niobium cavity with both ends of the beam pipes covered with metal plates were measured, showing great agreement with the numerical computation results. The electromagnetic fields of the trapped modes along the cavity's central axis were also examined to understand how the particle beam would be affected.